Higher-order derivative estimates for the heat equation on a smooth domain
Abstract
We consider the linear heat equation on a bounded domain and on an exterior domain. We study estimates of any order derivatives of the solution locally in time in the Lebesgue spaces. We give a proof of the estimates in the end-point cases p = 1, ∞. We also obtain derivative estimates for the equation with the fractional Dirichlet Laplacian.
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